Components of Braids

A braid is build from simpler units that mathematicians call components. Each unique way of crossing the strands of a braid is called a component.

In the real world, people braid rope to make it stronger, they braid their hair to make it look nice and keep it from flying about in the wind, or they may braid strands of fiber to make friendship bracelets or other attractive weavings. Do you know how to do any of these kinds of braiding? Can you list the components of a type of braid you know how to make? Listing the components is actually a good way to give directions for how to make the braid.

Perhaps you noticed that there is a pattern to the list of components for a braid to strengthen rope, make someone's hair look nice, or produce a weaving. You could invent ways to make such braids without a pattern, but the rope might not be as strong as it could be, and the hair or the weaving might look kind of random, knotted and strange. When mathematicians are studying braids and knots, however, there is not such a need to be limited to braids that show obvious patterns. Instead, all imaginable braids are of interest.

Think about this: